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<div class="subTitle">org.apache.commons.math3.stat.correlation</div>
<h2 title="Class KendallsCorrelation" class="title">Class KendallsCorrelation</h2>
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<pre>public class <span class="strong">KendallsCorrelation</span>
extends <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></pre>
<div class="block">Implementation of Kendall's Tau-b rank correlation</a>.
 <p>
 A pair of observations (x<sub>1</sub>, y<sub>1</sub>) and
 (x<sub>2</sub>, y<sub>2</sub>) are considered <i>concordant</i> if
 x<sub>1</sub> &lt; x<sub>2</sub> and y<sub>1</sub> &lt; y<sub>2</sub>
 or x<sub>2</sub> &lt; x<sub>1</sub> and y<sub>2</sub> &lt; y<sub>1</sub>.
 The pair is <i>discordant</i> if x<sub>1</sub> &lt; x<sub>2</sub> and
 y<sub>2</sub> &lt; y<sub>1</sub> or x<sub>2</sub> &lt; x<sub>1</sub> and
 y<sub>1</sub> &lt; y<sub>2</sub>.  If either x<sub>1</sub> = x<sub>2</sub>
 or y<sub>1</sub> = y<sub>2</sub>, the pair is neither concordant nor
 discordant.
 <p>
 Kendall's Tau-b is defined as:
 <pre>
 tau<sub>b</sub> = (n<sub>c</sub> - n<sub>d</sub>) / sqrt((n<sub>0</sub> - n<sub>1</sub>) * (n<sub>0</sub> - n<sub>2</sub>))
 </pre>
 <p>
 where:
 <ul>
     <li>n<sub>0</sub> = n * (n - 1) / 2</li>
     <li>n<sub>c</sub> = Number of concordant pairs</li>
     <li>n<sub>d</sub> = Number of discordant pairs</li>
     <li>n<sub>1</sub> = sum of t<sub>i</sub> * (t<sub>i</sub> - 1) / 2 for all i</li>
     <li>n<sub>2</sub> = sum of u<sub>j</sub> * (u<sub>j</sub> - 1) / 2 for all j</li>
     <li>t<sub>i</sub> = Number of tied values in the i<sup>th</sup> group of ties in x</li>
     <li>u<sub>j</sub> = Number of tied values in the j<sup>th</sup> group of ties in y</li>
 </ul>
 <p>
 This implementation uses the O(n log n) algorithm described in
 William R. Knight's 1966 paper "A Computer Method for Calculating
 Kendall's Tau with Ungrouped Data" in the Journal of the American
 Statistical Association.</div>
<dl><dt><span class="strong">Since:</span></dt>
  <dd>3.3</dd>
<dt><span class="strong">Version:</span></dt>
  <dd>$Id: KendallsCorrelation.java 1548907 2013-12-07 13:08:06Z tn $</dd>
<dt><span class="strong">See Also:</span></dt><dd><a href="http://en.wikipedia.org/wiki/Kendall_tau_rank_correlation_coefficient">
 Kendall tau rank correlation coefficient (Wikipedia)</a>, 
<a href="http://www.jstor.org/stable/2282833">A Computer
 Method for Calculating Kendall's Tau with Ungrouped Data</a></dd></dl>
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<td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/correlation/KendallsCorrelation.html#KendallsCorrelation()">KendallsCorrelation</a></strong>()</code>
<div class="block">Create a KendallsCorrelation instance without data.</div>
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<td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/correlation/KendallsCorrelation.html#KendallsCorrelation(double[][])">KendallsCorrelation</a></strong>(double[][]&nbsp;data)</code>
<div class="block">Create a KendallsCorrelation from a rectangular array
 whose columns represent values of variables to be correlated.</div>
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<td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/correlation/KendallsCorrelation.html#KendallsCorrelation(org.apache.commons.math3.linear.RealMatrix)">KendallsCorrelation</a></strong>(<a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;matrix)</code>
<div class="block">Create a KendallsCorrelation from a RealMatrix whose columns
 represent variables to be correlated.</div>
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<td class="colFirst"><code><a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/correlation/KendallsCorrelation.html#computeCorrelationMatrix(double[][])">computeCorrelationMatrix</a></strong>(double[][]&nbsp;matrix)</code>
<div class="block">Computes the Kendall's Tau rank correlation matrix for the columns of
 the input rectangular array.</div>
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<td class="colFirst"><code><a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/correlation/KendallsCorrelation.html#computeCorrelationMatrix(org.apache.commons.math3.linear.RealMatrix)">computeCorrelationMatrix</a></strong>(<a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;matrix)</code>
<div class="block">Computes the Kendall's Tau rank correlation matrix for the columns of
 the input matrix.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/correlation/KendallsCorrelation.html#correlation(double[], double[])">correlation</a></strong>(double[]&nbsp;xArray,
           double[]&nbsp;yArray)</code>
<div class="block">Computes the Kendall's Tau rank correlation coefficient between the two arrays.</div>
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<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/correlation/KendallsCorrelation.html#getCorrelationMatrix()">getCorrelationMatrix</a></strong>()</code>
<div class="block">Returns the correlation matrix.</div>
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<pre>public&nbsp;KendallsCorrelation()</pre>
<div class="block">Create a KendallsCorrelation instance without data.</div>
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<h4>KendallsCorrelation</h4>
<pre>public&nbsp;KendallsCorrelation(double[][]&nbsp;data)</pre>
<div class="block">Create a KendallsCorrelation from a rectangular array
 whose columns represent values of variables to be correlated.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>data</code> - rectangular array with columns representing variables</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="http://docs.oracle.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</a></code> - if the input data array is not
 rectangular with at least two rows and two columns.</dd></dl>
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<pre>public&nbsp;KendallsCorrelation(<a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;matrix)</pre>
<div class="block">Create a KendallsCorrelation from a RealMatrix whose columns
 represent variables to be correlated.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>matrix</code> - matrix with columns representing variables to correlate</dd></dl>
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<h4>getCorrelationMatrix</h4>
<pre>public&nbsp;<a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;getCorrelationMatrix()</pre>
<div class="block">Returns the correlation matrix.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>correlation matrix</dd></dl>
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<h4>computeCorrelationMatrix</h4>
<pre>public&nbsp;<a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;computeCorrelationMatrix(<a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;matrix)</pre>
<div class="block">Computes the Kendall's Tau rank correlation matrix for the columns of
 the input matrix.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>matrix</code> - matrix with columns representing variables to correlate</dd>
<dt><span class="strong">Returns:</span></dt><dd>correlation matrix</dd></dl>
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<h4>computeCorrelationMatrix</h4>
<pre>public&nbsp;<a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;computeCorrelationMatrix(double[][]&nbsp;matrix)</pre>
<div class="block">Computes the Kendall's Tau rank correlation matrix for the columns of
 the input rectangular array.  The columns of the array represent values
 of variables to be correlated.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>matrix</code> - matrix with columns representing variables to correlate</dd>
<dt><span class="strong">Returns:</span></dt><dd>correlation matrix</dd></dl>
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<h4>correlation</h4>
<pre>public&nbsp;double&nbsp;correlation(double[]&nbsp;xArray,
                 double[]&nbsp;yArray)
                   throws <a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></pre>
<div class="block">Computes the Kendall's Tau rank correlation coefficient between the two arrays.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>xArray</code> - first data array</dd><dd><code>yArray</code> - second data array</dd>
<dt><span class="strong">Returns:</span></dt><dd>Returns Kendall's Tau rank correlation coefficient for the two arrays</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the arrays lengths do not match</dd></dl>
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